{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 导入数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 数据处理最重要的模块\n",
    "import pandas as pd # 数据处理最重要的模块\n",
    "import scipy.stats as stats # 统计模块\n",
    "import scipy\n",
    "# import pymysql  # 导入数据库模块\n",
    "\n",
    "from datetime import datetime # 时间模块\n",
    "import statsmodels.formula.api as smf  # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt  # 画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "from matplotlib.font_manager import FontProperties # 作图中文\n",
    "from pylab import mpl\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "from pandas.tseries.offsets import MonthEnd\n",
    "\n",
    "#输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell # jupyter运行输出的模块\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Preclose</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1982-09-20</th>\n",
       "      <td>122.55</td>\n",
       "      <td>123.25</td>\n",
       "      <td>120.81</td>\n",
       "      <td>122.51</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-21</th>\n",
       "      <td>122.51</td>\n",
       "      <td>125.27</td>\n",
       "      <td>122.16</td>\n",
       "      <td>124.88</td>\n",
       "      <td>122.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-22</th>\n",
       "      <td>124.88</td>\n",
       "      <td>127.31</td>\n",
       "      <td>123.56</td>\n",
       "      <td>123.99</td>\n",
       "      <td>124.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-23</th>\n",
       "      <td>123.99</td>\n",
       "      <td>124.92</td>\n",
       "      <td>122.21</td>\n",
       "      <td>123.81</td>\n",
       "      <td>123.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-24</th>\n",
       "      <td>123.81</td>\n",
       "      <td>124.44</td>\n",
       "      <td>122.36</td>\n",
       "      <td>123.32</td>\n",
       "      <td>123.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-25</th>\n",
       "      <td>5984.63</td>\n",
       "      <td>6040.10</td>\n",
       "      <td>5981.44</td>\n",
       "      <td>6040.04</td>\n",
       "      <td>6040.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-26</th>\n",
       "      <td>6024.97</td>\n",
       "      <td>6049.75</td>\n",
       "      <td>6007.37</td>\n",
       "      <td>6037.59</td>\n",
       "      <td>6040.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-27</th>\n",
       "      <td>6006.17</td>\n",
       "      <td>6006.17</td>\n",
       "      <td>5932.95</td>\n",
       "      <td>5970.84</td>\n",
       "      <td>6037.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-30</th>\n",
       "      <td>5920.67</td>\n",
       "      <td>5940.79</td>\n",
       "      <td>5869.16</td>\n",
       "      <td>5906.94</td>\n",
       "      <td>5970.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>5919.74</td>\n",
       "      <td>5929.74</td>\n",
       "      <td>5868.86</td>\n",
       "      <td>5881.63</td>\n",
       "      <td>5906.94</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10661 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Open  Highest   Lowest    Close  Preclose\n",
       "Day                                                     \n",
       "1982-09-20   122.55   123.25   120.81   122.51       NaN\n",
       "1982-09-21   122.51   125.27   122.16   124.88    122.51\n",
       "1982-09-22   124.88   127.31   123.56   123.99    124.88\n",
       "1982-09-23   123.99   124.92   122.21   123.81    123.99\n",
       "1982-09-24   123.81   124.44   122.36   123.32    123.81\n",
       "...             ...      ...      ...      ...       ...\n",
       "2024-12-25  5984.63  6040.10  5981.44  6040.04   6040.04\n",
       "2024-12-26  6024.97  6049.75  6007.37  6037.59   6040.04\n",
       "2024-12-27  6006.17  6006.17  5932.95  5970.84   6037.59\n",
       "2024-12-30  5920.67  5940.79  5869.16  5906.94   5970.84\n",
       "2024-12-31  5919.74  5929.74  5868.86  5881.63   5906.94\n",
       "\n",
       "[10661 rows x 5 columns]"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('datasets/SPX.csv')\n",
    "data['Day']=pd.to_datetime(data['Day'],format='%Y/%m/%d')\n",
    "data.set_index('Day',inplace=True)\n",
    "data['Close']=pd.to_numeric(data['Close'],errors='coerce')\n",
    "data['Preclose']=(data['Close']).shift(1)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1982-09-20</th>\n",
       "      <td>122.55</td>\n",
       "      <td>123.25</td>\n",
       "      <td>120.81</td>\n",
       "      <td>122.51</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-21</th>\n",
       "      <td>122.51</td>\n",
       "      <td>125.27</td>\n",
       "      <td>122.16</td>\n",
       "      <td>124.88</td>\n",
       "      <td>122.51</td>\n",
       "      <td>0.019345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-22</th>\n",
       "      <td>124.88</td>\n",
       "      <td>127.31</td>\n",
       "      <td>123.56</td>\n",
       "      <td>123.99</td>\n",
       "      <td>124.88</td>\n",
       "      <td>-0.007127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-23</th>\n",
       "      <td>123.99</td>\n",
       "      <td>124.92</td>\n",
       "      <td>122.21</td>\n",
       "      <td>123.81</td>\n",
       "      <td>123.99</td>\n",
       "      <td>-0.001452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-09-24</th>\n",
       "      <td>123.81</td>\n",
       "      <td>124.44</td>\n",
       "      <td>122.36</td>\n",
       "      <td>123.32</td>\n",
       "      <td>123.81</td>\n",
       "      <td>-0.003958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-25</th>\n",
       "      <td>5984.63</td>\n",
       "      <td>6040.10</td>\n",
       "      <td>5981.44</td>\n",
       "      <td>6040.04</td>\n",
       "      <td>6040.04</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-26</th>\n",
       "      <td>6024.97</td>\n",
       "      <td>6049.75</td>\n",
       "      <td>6007.37</td>\n",
       "      <td>6037.59</td>\n",
       "      <td>6040.04</td>\n",
       "      <td>-0.000406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-27</th>\n",
       "      <td>6006.17</td>\n",
       "      <td>6006.17</td>\n",
       "      <td>5932.95</td>\n",
       "      <td>5970.84</td>\n",
       "      <td>6037.59</td>\n",
       "      <td>-0.011056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-30</th>\n",
       "      <td>5920.67</td>\n",
       "      <td>5940.79</td>\n",
       "      <td>5869.16</td>\n",
       "      <td>5906.94</td>\n",
       "      <td>5970.84</td>\n",
       "      <td>-0.010702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>5919.74</td>\n",
       "      <td>5929.74</td>\n",
       "      <td>5868.86</td>\n",
       "      <td>5881.63</td>\n",
       "      <td>5906.94</td>\n",
       "      <td>-0.004285</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10661 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Open  Highest   Lowest    Close  Preclose  Raw_return\n",
       "Day                                                                 \n",
       "1982-09-20   122.55   123.25   120.81   122.51       NaN         NaN\n",
       "1982-09-21   122.51   125.27   122.16   124.88    122.51    0.019345\n",
       "1982-09-22   124.88   127.31   123.56   123.99    124.88   -0.007127\n",
       "1982-09-23   123.99   124.92   122.21   123.81    123.99   -0.001452\n",
       "1982-09-24   123.81   124.44   122.36   123.32    123.81   -0.003958\n",
       "...             ...      ...      ...      ...       ...         ...\n",
       "2024-12-25  5984.63  6040.10  5981.44  6040.04   6040.04    0.000000\n",
       "2024-12-26  6024.97  6049.75  6007.37  6037.59   6040.04   -0.000406\n",
       "2024-12-27  6006.17  6006.17  5932.95  5970.84   6037.59   -0.011056\n",
       "2024-12-30  5920.67  5940.79  5869.16  5906.94   5970.84   -0.010702\n",
       "2024-12-31  5919.74  5929.74  5868.86  5881.63   5906.94   -0.004285\n",
       "\n",
       "[10661 rows x 6 columns]"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['Raw_return'] = data['Close'] / data['Preclose'] - 1\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1926-01-01</th>\n",
       "      <td>0.000561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-02-01</th>\n",
       "      <td>-0.033046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-03-01</th>\n",
       "      <td>-0.064002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-04-01</th>\n",
       "      <td>0.037029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-05-01</th>\n",
       "      <td>0.012095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-01</th>\n",
       "      <td>-0.020300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-01</th>\n",
       "      <td>-0.048003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-10-01</th>\n",
       "      <td>-0.029225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-01</th>\n",
       "      <td>0.093358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-01</th>\n",
       "      <td>0.053768</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1176 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   r\n",
       "month               \n",
       "1926-01-01  0.000561\n",
       "1926-02-01 -0.033046\n",
       "1926-03-01 -0.064002\n",
       "1926-04-01  0.037029\n",
       "1926-05-01  0.012095\n",
       "...              ...\n",
       "2023-08-01 -0.020300\n",
       "2023-09-01 -0.048003\n",
       "2023-10-01 -0.029225\n",
       "2023-11-01  0.093358\n",
       "2023-12-01  0.053768\n",
       "\n",
       "[1176 rows x 1 columns]"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "US_market_ret = pd.read_csv('datasets/US stock market return.csv')\n",
    "US_market_ret['month'] = pd.to_datetime(US_market_ret['month'],format='%Y-%m-%d')\n",
    "US_market_ret.set_index('month',inplace=True)\n",
    "US_market_ret.sort_index(inplace=True)\n",
    "US_market_ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Raw_return</th>\n",
       "      <th>r</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1982-10-01</th>\n",
       "      <td>120.42</td>\n",
       "      <td>122.46</td>\n",
       "      <td>119.13</td>\n",
       "      <td>121.97</td>\n",
       "      <td>120.42</td>\n",
       "      <td>0.012872</td>\n",
       "      <td>0.118632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-11-01</th>\n",
       "      <td>133.71</td>\n",
       "      <td>136.03</td>\n",
       "      <td>132.54</td>\n",
       "      <td>135.47</td>\n",
       "      <td>133.71</td>\n",
       "      <td>0.013163</td>\n",
       "      <td>0.051941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-12-01</th>\n",
       "      <td>138.54</td>\n",
       "      <td>141.24</td>\n",
       "      <td>137.31</td>\n",
       "      <td>138.72</td>\n",
       "      <td>138.54</td>\n",
       "      <td>0.001299</td>\n",
       "      <td>0.014510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1983-02-01</th>\n",
       "      <td>145.30</td>\n",
       "      <td>146.04</td>\n",
       "      <td>142.57</td>\n",
       "      <td>142.96</td>\n",
       "      <td>145.30</td>\n",
       "      <td>-0.016105</td>\n",
       "      <td>0.030215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1983-03-01</th>\n",
       "      <td>148.06</td>\n",
       "      <td>151.75</td>\n",
       "      <td>148.05</td>\n",
       "      <td>150.88</td>\n",
       "      <td>148.06</td>\n",
       "      <td>0.019046</td>\n",
       "      <td>0.034678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-06-01</th>\n",
       "      <td>4183.03</td>\n",
       "      <td>4232.43</td>\n",
       "      <td>4171.64</td>\n",
       "      <td>4221.02</td>\n",
       "      <td>4179.83</td>\n",
       "      <td>0.009854</td>\n",
       "      <td>0.067583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-01</th>\n",
       "      <td>4578.83</td>\n",
       "      <td>4584.62</td>\n",
       "      <td>4567.53</td>\n",
       "      <td>4576.73</td>\n",
       "      <td>4588.96</td>\n",
       "      <td>-0.002665</td>\n",
       "      <td>-0.020300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-01</th>\n",
       "      <td>4530.60</td>\n",
       "      <td>4541.25</td>\n",
       "      <td>4501.35</td>\n",
       "      <td>4515.77</td>\n",
       "      <td>4507.66</td>\n",
       "      <td>0.001799</td>\n",
       "      <td>-0.048003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-01</th>\n",
       "      <td>4201.27</td>\n",
       "      <td>4245.64</td>\n",
       "      <td>4197.74</td>\n",
       "      <td>4237.86</td>\n",
       "      <td>4193.80</td>\n",
       "      <td>0.010506</td>\n",
       "      <td>0.093358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-01</th>\n",
       "      <td>4559.43</td>\n",
       "      <td>4599.39</td>\n",
       "      <td>4554.71</td>\n",
       "      <td>4594.63</td>\n",
       "      <td>4567.80</td>\n",
       "      <td>0.005874</td>\n",
       "      <td>0.053768</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>318 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Open  Highest   Lowest    Close  Preclose  Raw_return         r\n",
       "1982-10-01   120.42   122.46   119.13   121.97    120.42    0.012872  0.118632\n",
       "1982-11-01   133.71   136.03   132.54   135.47    133.71    0.013163  0.051941\n",
       "1982-12-01   138.54   141.24   137.31   138.72    138.54    0.001299  0.014510\n",
       "1983-02-01   145.30   146.04   142.57   142.96    145.30   -0.016105  0.030215\n",
       "1983-03-01   148.06   151.75   148.05   150.88    148.06    0.019046  0.034678\n",
       "...             ...      ...      ...      ...       ...         ...       ...\n",
       "2023-06-01  4183.03  4232.43  4171.64  4221.02   4179.83    0.009854  0.067583\n",
       "2023-08-01  4578.83  4584.62  4567.53  4576.73   4588.96   -0.002665 -0.020300\n",
       "2023-09-01  4530.60  4541.25  4501.35  4515.77   4507.66    0.001799 -0.048003\n",
       "2023-11-01  4201.27  4245.64  4197.74  4237.86   4193.80    0.010506  0.093358\n",
       "2023-12-01  4559.43  4599.39  4554.71  4594.63   4567.80    0.005874  0.053768\n",
       "\n",
       "[318 rows x 7 columns]"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data=pd.merge(data,US_market_ret,left_index=True,right_index=True)\n",
    "Month_data=Month_data['1982':]\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 描述性统计"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 均值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012183779874213837"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(Month_data['1982':'2023']['r'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 分位数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.0377365,\n",
       " -0.0207086,\n",
       " -0.0028741999999999995,\n",
       " 0.008912400000000001,\n",
       " 0.016625499999999998,\n",
       " 0.0243092,\n",
       " 0.0331395,\n",
       " 0.0434166,\n",
       " 0.0638819]"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statistics import quantiles\n",
    "quantiles(Month_data['1982':'2023']['r'],n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 方差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1982-09-30</th>\n",
       "      <td>0.000099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-10-31</th>\n",
       "      <td>0.000294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-11-30</th>\n",
       "      <td>0.000271</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-12-31</th>\n",
       "      <td>0.000118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1983-01-31</th>\n",
       "      <td>0.000161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.000076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>0.000048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.000058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.000077</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>508 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Variance\n",
       "Day                 \n",
       "1982-09-30  0.000099\n",
       "1982-10-31  0.000294\n",
       "1982-11-30  0.000271\n",
       "1982-12-31  0.000118\n",
       "1983-01-31  0.000161\n",
       "...              ...\n",
       "2024-08-31  0.000150\n",
       "2024-09-30  0.000076\n",
       "2024-10-31  0.000048\n",
       "2024-11-30  0.000058\n",
       "2024-12-31  0.000077\n",
       "\n",
       "[508 rows x 1 columns]"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_var = data.resample('ME')['Raw_return'].var().to_frame()\n",
    "monthly_var.rename(columns={'Raw_return':'Variance'},inplace=True)\n",
    "monthly_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 统计性检验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=5.038843534223295, pvalue=7.883430387265631e-07, df=317)"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Month_data['r'],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9468937649035656"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['r'].skew()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 直方图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  3.,   7.,  35., 259., 676., 178.,  13.,   2.,   0.,   3.]),\n",
       " array([-0.291731 , -0.2231436, -0.1545562, -0.0859688, -0.0173814,\n",
       "         0.051206 ,  0.1197934,  0.1883808,  0.2569682,  0.3255556,\n",
       "         0.394143 ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'histogram')"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data=US_market_ret\n",
    "plt.hist(data)\n",
    "plt.title('histogram')\n",
    "plt.show()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 折线图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
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   "source": [
    "fig, ax = plt.subplots(figsize=(15,4))\n",
    "\n",
    "ax.plot('r',#图片数据\n",
    "'.-',#图片类型，可以改成*--等，\n",
    "color='blue',#图片颜色\n",
    "label='Monthly Return',#图片标签\n",
    "linewidth=1,#图片线宽\n",
    "data=Month_data)#图片数据来源\n",
    "ax.set_title(\"US Market Ret\")\n",
    "ax.set_ylabel('r')#图片y轴标签\n",
    "ax.set_xlabel('Year')#图片x轴标签\n",
    "#设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax.xaxis.set_major_formatter(data_format)\n",
    "ax.xaxis.set_major_locator(mdates.YearLocator())\n",
    "#转置x轴的日期显示格式\n",
    "plt.xticks(rotation=90)\n",
    "#添加图例\n",
    "plt.legend(loc='upper right',fontsize= 8)\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 美国股票市场收益率的可预测性"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 理论论述"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "失业率\n",
    "\n",
    "\n",
    "•失业率是衡量经济健康状况的重要指标之一，低失业率通常意味着经济活动较为活跃，企业盈利能力较强，从而可能推动股票价格上涨。\n",
    "\n",
    "\n",
    "• 失业率与消费者支出密切相关，高失业率可能导致消费者减少支出，进而影响企业的收入和利润，从而对股票市场产生负面影响。\n",
    "\n",
    "\n",
    "• 失业率的变化会影响政府和中央银行的政策决策。例如，高失业率可能导致政府采取刺激措施或中央银行降低利率，以促进经济增长和就业。\n",
    "\n",
    "\n",
    "CPI\n",
    "\n",
    "\n",
    "• CPI是衡量通货膨胀水平的重要指标。通货膨胀率的上升会增加企业的生产成本，降低其利润，从而可能对股票市场产生负面影响。\n",
    "\n",
    "\n",
    "• 美联储等中央银行会根据CPI的变化来调整货币政策。高通胀可能导致加息，从而增加企业的融资成本和投资者的预期收益率，对股票市场产生压力。\n",
    "\n",
    "\n",
    "•CPI的变化会影响投资者对未来经济和企业盈利的预期。例如，持续上升的CPI可能导致投资者对经济前景持谨慎态度，从而影响股票市场的表现。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型\n",
    "\n",
    "\n",
    "$r_{t}=\\alpha+\\beta*x_{t-1}+\\epsilon_t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UR</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1970-01-01</th>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970-02-01</th>\n",
       "      <td>3.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970-03-01</th>\n",
       "      <td>4.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970-04-01</th>\n",
       "      <td>4.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970-05-01</th>\n",
       "      <td>4.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-02</th>\n",
       "      <td>4.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-06</th>\n",
       "      <td>4.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-04</th>\n",
       "      <td>4.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-01</th>\n",
       "      <td>4.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-06</th>\n",
       "      <td>4.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>660 rows × 1 columns</p>\n",
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      "text/plain": [
       "             UR\n",
       "Day            \n",
       "1970-01-01  3.5\n",
       "1970-02-01  3.9\n",
       "1970-03-01  4.2\n",
       "1970-04-01  4.4\n",
       "1970-05-01  4.6\n",
       "...         ...\n",
       "2024-08-02  4.3\n",
       "2024-09-06  4.2\n",
       "2024-10-04  4.1\n",
       "2024-11-01  4.1\n",
       "2024-12-06  4.2\n",
       "\n",
       "[660 rows x 1 columns]"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UR=pd.read_csv('datasets/UR.csv')#UR是失业率\n",
    "UR['Day']=pd.to_datetime(UR['Day'],format='%Y-%m-%d')\n",
    "UR.set_index('Day',inplace=True)\n",
    "UR.sort_values(by=['Day'],axis=0,ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1982-01-01</th>\n",
       "      <td>-0.026209</td>\n",
       "      <td>8.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-02-01</th>\n",
       "      <td>-0.051126</td>\n",
       "      <td>8.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-03-01</th>\n",
       "      <td>-0.010101</td>\n",
       "      <td>8.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-04-01</th>\n",
       "      <td>0.043269</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-05-01</th>\n",
       "      <td>-0.028213</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-01</th>\n",
       "      <td>0.006041</td>\n",
       "      <td>3.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-02-01</th>\n",
       "      <td>0.033401</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-11-01</th>\n",
       "      <td>0.036130</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-04-01</th>\n",
       "      <td>-0.090973</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-01</th>\n",
       "      <td>-0.048003</td>\n",
       "      <td>3.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>331 rows × 2 columns</p>\n",
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      ],
      "text/plain": [
       "                   r   UR\n",
       "1982-01-01 -0.026209  8.5\n",
       "1982-02-01 -0.051126  8.6\n",
       "1982-03-01 -0.010101  8.9\n",
       "1982-04-01  0.043269  9.0\n",
       "1982-05-01 -0.028213  9.3\n",
       "...              ...  ...\n",
       "2018-06-01  0.006041  3.8\n",
       "2019-02-01  0.033401  4.0\n",
       "2019-11-01  0.036130  3.6\n",
       "2022-04-01 -0.090973  3.6\n",
       "2023-09-01 -0.048003  3.8\n",
       "\n",
       "[331 rows x 2 columns]"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data=pd.merge(US_market_ret,UR,left_index=True,right_index=True)\n",
    "reg_data=reg_data['1982':'2023']\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
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       "    </g>\n",
       "    <g id=\"xtick_22\">\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"443.573038\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- 2001 -->\n",
       "      <g transform=\"translate(446.332413 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_23\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"461.823256\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 2002 -->\n",
       "      <g transform=\"translate(464.582631 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_24\">\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"480.073474\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 2003 -->\n",
       "      <g transform=\"translate(482.832849 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-33\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_25\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"498.323692\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_25\">\n",
       "      <!-- 2004 -->\n",
       "      <g transform=\"translate(501.083067 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-34\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_26\">\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"516.623911\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_26\">\n",
       "      <!-- 2005 -->\n",
       "      <g transform=\"translate(519.383286 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_27\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"534.874129\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_27\">\n",
       "      <!-- 2006 -->\n",
       "      <g transform=\"translate(537.633504 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-36\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_28\">\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"553.124347\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_28\">\n",
       "      <!-- 2007 -->\n",
       "      <g transform=\"translate(555.883722 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-37\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_29\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"571.374565\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_29\">\n",
       "      <!-- 2008 -->\n",
       "      <g transform=\"translate(574.13394 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-38\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_30\">\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"589.674783\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_30\">\n",
       "      <!-- 2009 -->\n",
       "      <g transform=\"translate(592.434158 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_31\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"607.925001\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_31\">\n",
       "      <!-- 2010 -->\n",
       "      <g transform=\"translate(610.684376 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_32\">\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"626.175219\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_32\">\n",
       "      <!-- 2011 -->\n",
       "      <g transform=\"translate(628.934594 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_33\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"644.425438\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
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       "      <!-- 2012 -->\n",
       "      <g transform=\"translate(647.184813 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_34\">\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"662.725656\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
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       "      <!-- 2013 -->\n",
       "      <g transform=\"translate(665.485031 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-33\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_35\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"680.975874\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "     </g>\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-34\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_36\">\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"699.226092\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "     </g>\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_37\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"717.47631\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
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       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_38\">\n",
       "     <g id=\"line2d_38\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"735.776529\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-37\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_39\">\n",
       "     <g id=\"line2d_39\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"754.026747\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_40\">\n",
       "     <g id=\"line2d_40\">\n",
       "      <g>\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_41\">\n",
       "     <g id=\"line2d_41\">\n",
       "      <g>\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_42\">\n",
       "     <g id=\"line2d_42\">\n",
       "      <g>\n",
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       "       <use xlink:href=\"#DejaVuSans-32\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"190.869141\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_43\">\n",
       "     <g id=\"line2d_43\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"827.07762\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-32\" x=\"127.246094\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_44\">\n",
       "     <g id=\"line2d_44\">\n",
       "      <g>\n",
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       "       <use xlink:href=\"#DejaVuSans-32\" x=\"127.246094\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_45\">\n",
       "     <g id=\"line2d_45\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mf217c87b9c\" x=\"863.578056\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "<Figure size 1500x600 with 2 Axes>"
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    "fig, ax1=plt.subplots(figsize=(15,6))\n",
    "\n",
    "\n",
    "ax1.plot(reg_data['r'],\n",
    "         label='r',\n",
    "         color='red',\n",
    "         linewidth=1,\n",
    "         linestyle='-',\n",
    "         marker='o')\n",
    "ax1.set_ylabel('r',color='red')\n",
    "\n",
    "\n",
    "data_format=mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "ax2=ax1.twinx()\n",
    "ax2.plot(reg_data['UR'].shift(1),\n",
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    "         linewidth=1,\n",
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    "         marker='o')\n",
    "ax2.set_ylabel('UR',color='blue')\n",
    "\n",
    "\n",
    "plt.title(\"America r and UR\")\n",
    "\n",
    "\n",
    "lines,labels=ax1.get_legend_handles_labels()\n",
    "lines2,labels2=ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines+lines2,labels+labels2,loc='upper right')\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
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       "             cpi\n",
       "Day             \n",
       "1980-01-01  13.9\n",
       "1980-02-01  14.2\n",
       "1980-03-01  14.8\n",
       "1980-04-01  14.7\n",
       "1980-05-01  14.4\n",
       "...          ...\n",
       "2023-11-01   3.1\n",
       "2023-12-01   3.4\n",
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       "2024-02-01   3.2\n",
       "2024-03-01   3.5\n",
       "\n",
       "[531 rows x 1 columns]"
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     },
     "execution_count": 152,
     "metadata": {},
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    "cpi=pd.read_csv('D:/Pythonclasshomework/python-homework-gyt/datasets/cpi .csv')\n",
    "cpi['Day']=pd.to_datetime(cpi['Day'],format='%Y/%m/%d')\n",
    "cpi.set_index('Day',inplace=True)\n",
    "cpi.sort_values(by=['Day'],axis=0,ascending=True)"
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  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
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       "                   r  cpi\n",
       "1982-01-01 -0.026209  8.4\n",
       "1982-02-01 -0.051126  7.6\n",
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       "\n",
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     "execution_count": 153,
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   "source": [
    "qreg_data=pd.merge(US_market_ret,cpi,left_index=True,right_index=True)\n",
    "qreg_data=qreg_data['1982':'2023']\n",
    "qreg_data"
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  {
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   "execution_count": 158,
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       "       <use xlink:href=\"#DejaVuSans-34\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"350.829696\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 1995 -->\n",
       "      <g transform=\"translate(353.589071 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-31\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"370.18088\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- 1996 -->\n",
       "      <g transform=\"translate(372.940255 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-31\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-36\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_18\">\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"389.58508\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_18\">\n",
       "      <!-- 1997 -->\n",
       "      <g transform=\"translate(392.344455 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-31\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-37\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_19\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"408.936264\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- 1998 -->\n",
       "      <g transform=\"translate(411.695639 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-31\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-38\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_20\">\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"428.287448\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 1999 -->\n",
       "      <g transform=\"translate(431.046823 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-31\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_21\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"447.638632\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_21\">\n",
       "      <!-- 2000 -->\n",
       "      <g transform=\"translate(450.398007 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_22\">\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"467.042833\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- 2001 -->\n",
       "      <g transform=\"translate(469.802208 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_23\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"486.394016\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 2002 -->\n",
       "      <g transform=\"translate(489.153391 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_24\">\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"505.7452\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 2003 -->\n",
       "      <g transform=\"translate(508.504575 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-33\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_25\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"525.096384\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_25\">\n",
       "      <!-- 2004 -->\n",
       "      <g transform=\"translate(527.855759 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-34\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_26\">\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"544.500585\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_26\">\n",
       "      <!-- 2005 -->\n",
       "      <g transform=\"translate(547.25996 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_27\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"563.851768\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_27\">\n",
       "      <!-- 2006 -->\n",
       "      <g transform=\"translate(566.611143 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-36\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_28\">\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"583.202952\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_28\">\n",
       "      <!-- 2007 -->\n",
       "      <g transform=\"translate(585.962327 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-37\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_29\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"602.554136\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_29\">\n",
       "      <!-- 2008 -->\n",
       "      <g transform=\"translate(605.313511 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-38\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_30\">\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"621.958337\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_30\">\n",
       "      <!-- 2009 -->\n",
       "      <g transform=\"translate(624.717712 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_31\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"641.309521\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_31\">\n",
       "      <!-- 2010 -->\n",
       "      <g transform=\"translate(644.068896 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_32\">\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"660.660704\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_32\">\n",
       "      <!-- 2011 -->\n",
       "      <g transform=\"translate(663.420079 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_33\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"680.011888\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_33\">\n",
       "      <!-- 2012 -->\n",
       "      <g transform=\"translate(682.771263 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_34\">\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"699.416089\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
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       "      <!-- 2013 -->\n",
       "      <g transform=\"translate(702.175464 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-33\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_35\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"718.767273\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_35\">\n",
       "      <!-- 2014 -->\n",
       "      <g transform=\"translate(721.526648 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-34\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_36\">\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"738.118456\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "     </g>\n",
       "     <g id=\"text_36\">\n",
       "      <!-- 2015 -->\n",
       "      <g transform=\"translate(740.877831 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_37\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"757.46964\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "     </g>\n",
       "     <g id=\"text_37\">\n",
       "      <!-- 2016 -->\n",
       "      <g transform=\"translate(760.229015 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-36\" x=\"190.869141\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_38\">\n",
       "     <g id=\"line2d_38\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mcbd542ab0d\" x=\"776.873841\" y=\"354.958125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "     </g>\n",
       "     <g id=\"text_38\">\n",
       "      <!-- 2017 -->\n",
       "      <g transform=\"translate(779.633216 387.408125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" x=\"127.246094\"/>\n",
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       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_39\">\n",
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       "    <g id=\"text_65\">\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 1600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1=plt.subplots(figsize=(16,6))\n",
    "\n",
    "\n",
    "ax1.plot(qreg_data['r'],\n",
    "         label='r',\n",
    "         color='red',\n",
    "         linewidth=1,\n",
    "         linestyle='-',\n",
    "         marker='o')\n",
    "ax1.set_ylabel('r',color='red')\n",
    "\n",
    "\n",
    "data_format=mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "ax2=ax1.twinx()\n",
    "ax2.plot(qreg_data['cpi'].shift(1),\n",
    "         label='cpi',\n",
    "         color='blue',\n",
    "         linewidth=1,\n",
    "         linestyle='-',\n",
    "         marker='o')\n",
    "ax2.set_ylabel('cpi',color='blue')\n",
    "\n",
    "\n",
    "plt.title(\"America r and cpi\")\n",
    "\n",
    "\n",
    "lines,labels=ax1.get_legend_handles_labels()\n",
    "lines2,labels2=ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines+lines2,labels+labels2,loc='upper right')\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 描述性统计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    331.000\n",
       "mean       5.967\n",
       "std        1.485\n",
       "min        3.600\n",
       "25%        4.950\n",
       "50%        5.600\n",
       "75%        6.900\n",
       "max       10.800\n",
       "Name: UR, dtype: float64"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['UR'].describe().round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r     -0.784\n",
       "UR     1.070\n",
       "lUR    1.084\n",
       "dtype: float64"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "r      3.021\n",
       "UR     1.059\n",
       "lUR    1.077\n",
       "dtype: float64"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data.skew().round(3)\n",
    "reg_data.kurt().round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    504.000\n",
       "mean       2.938\n",
       "std        1.667\n",
       "min       -2.100\n",
       "25%        1.800\n",
       "50%        2.800\n",
       "75%        3.800\n",
       "max        9.100\n",
       "Name: cpi, dtype: float64"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qreg_data['cpi'].describe().round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r      -0.697\n",
       "cpi     0.740\n",
       "lcpi    0.741\n",
       "dtype: float64"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "r       2.257\n",
       "cpi     1.616\n",
       "lcpi    1.601\n",
       "dtype: float64"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qreg_data.skew().round(3)\n",
    "qreg_data.kurt().round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 统计性检验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=73.10075888060105, pvalue=6.635446151037506e-206, df=330)"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(reg_data['UR'],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0702747800875136"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['UR'].skew()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=39.5485149187398, pvalue=1.7495978557686518e-156, df=503)"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(qreg_data['cpi'],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7401591085878623"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qreg_data['cpi'].skew()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      r   R-squared:                       0.012\n",
      "Model:                            OLS   Adj. R-squared:                  0.009\n",
      "Method:                 Least Squares   F-statistic:                     3.951\n",
      "Date:                Sat, 04 Jan 2025   Prob (F-statistic):             0.0477\n",
      "Time:                        08:26:42   Log-Likelihood:                 572.08\n",
      "No. Observations:                 329   AIC:                            -1140.\n",
      "Df Residuals:                     327   BIC:                            -1133.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0084      0.010     -0.853      0.394      -0.028       0.011\n",
      "lUR            0.0032      0.002      1.988      0.048    3.26e-05       0.006\n",
      "==============================================================================\n",
      "Omnibus:                       54.568   Durbin-Watson:                   1.904\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              147.338\n",
      "Skew:                          -0.768   Prob(JB):                     1.01e-32\n",
      "Kurtosis:                       5.896   Cond. No.                         26.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "reg_data['lUR']=reg_data['UR'].shift(2) \n",
    "model_UR=smf.ols('r ~ lUR',data=reg_data).fit()\n",
    "print(model_UR.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      r   R-squared:                       0.006\n",
      "Model:                            OLS   Adj. R-squared:                  0.004\n",
      "Method:                 Least Squares   F-statistic:                     2.905\n",
      "Date:                Sat, 04 Jan 2025   Prob (F-statistic):             0.0889\n",
      "Time:                        08:34:43   Log-Likelihood:                 844.57\n",
      "No. Observations:                 502   AIC:                            -1685.\n",
      "Df Residuals:                     500   BIC:                            -1677.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0162      0.004      3.974      0.000       0.008       0.024\n",
      "lcpi          -0.0021      0.001     -1.704      0.089      -0.004       0.000\n",
      "==============================================================================\n",
      "Omnibus:                       61.608   Durbin-Watson:                   1.939\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              138.378\n",
      "Skew:                          -0.665   Prob(JB):                     8.95e-31\n",
      "Kurtosis:                       5.202   Cond. No.                         7.30\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "qreg_data['lcpi']=qreg_data['cpi'].shift(2) \n",
    "model_cpi=smf.ols('r ~ lcpi',data=qreg_data).fit()\n",
    "print(model_cpi.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>r</th>\n",
       "      <th>UR</th>\n",
       "      <th>lUR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-01</th>\n",
       "      <td>-0.070114</td>\n",
       "      <td>5.4</td>\n",
       "      <td>5.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-02-01</th>\n",
       "      <td>0.014900</td>\n",
       "      <td>5.4</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-03-01</th>\n",
       "      <td>0.024148</td>\n",
       "      <td>5.3</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-04-01</th>\n",
       "      <td>-0.028283</td>\n",
       "      <td>5.2</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-05-01</th>\n",
       "      <td>0.088935</td>\n",
       "      <td>5.4</td>\n",
       "      <td>5.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-01</th>\n",
       "      <td>0.006041</td>\n",
       "      <td>3.8</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-02-01</th>\n",
       "      <td>0.033401</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-11-01</th>\n",
       "      <td>0.036130</td>\n",
       "      <td>3.6</td>\n",
       "      <td>3.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-04-01</th>\n",
       "      <td>-0.090973</td>\n",
       "      <td>3.6</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-01</th>\n",
       "      <td>-0.048003</td>\n",
       "      <td>3.8</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>235 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   r   UR  lUR\n",
       "1990-01-01 -0.070114  5.4  5.3\n",
       "1990-02-01  0.014900  5.4  5.4\n",
       "1990-03-01  0.024148  5.3  5.4\n",
       "1990-04-01 -0.028283  5.2  5.4\n",
       "1990-05-01  0.088935  5.4  5.3\n",
       "...              ...  ...  ...\n",
       "2018-06-01  0.006041  3.8  5.0\n",
       "2019-02-01  0.033401  4.0  4.4\n",
       "2019-11-01  0.036130  3.6  3.8\n",
       "2022-04-01 -0.090973  3.6  4.0\n",
       "2023-09-01 -0.048003  3.8  3.6\n",
       "\n",
       "[235 rows x 3 columns]"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lreg_data=pd.merge(reg_data,UR,left_index=True,right_index=True)\n",
    "lreg_data=reg_data['1990':]\n",
    "lreg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      r   R-squared:                       0.008\n",
      "Model:                            OLS   Adj. R-squared:                  0.003\n",
      "Method:                 Least Squares   F-statistic:                     1.768\n",
      "Date:                Sat, 04 Jan 2025   Prob (F-statistic):              0.185\n",
      "Time:                        08:38:04   Log-Likelihood:                 417.14\n",
      "No. Observations:                 233   AIC:                            -830.3\n",
      "Df Residuals:                     231   BIC:                            -823.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0102      0.015     -0.698      0.486      -0.039       0.018\n",
      "lUR            0.0035      0.003      1.330      0.185      -0.002       0.009\n",
      "==============================================================================\n",
      "Omnibus:                       16.632   Durbin-Watson:                   1.918\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               19.197\n",
      "Skew:                          -0.574   Prob(JB):                     6.78e-05\n",
      "Kurtosis:                       3.812   Cond. No.                         31.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\18762\\AppData\\Local\\Temp\\ipykernel_2160\\449959950.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  lreg_data['lUR']=lreg_data['UR'].shift(2)\n"
     ]
    }
   ],
   "source": [
    "lreg_data['lUR']=lreg_data['UR'].shift(2) \n",
    "lmodel_UR=smf.ols('r ~ lUR',data=lreg_data).fit()\n",
    "print(lmodel_UR.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "      <th>cpi</th>\n",
       "      <th>lcpi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-01</th>\n",
       "      <td>-0.070114</td>\n",
       "      <td>5.2</td>\n",
       "      <td>4.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-02-01</th>\n",
       "      <td>0.014900</td>\n",
       "      <td>5.3</td>\n",
       "      <td>4.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-03-01</th>\n",
       "      <td>0.024148</td>\n",
       "      <td>5.2</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-04-01</th>\n",
       "      <td>-0.028283</td>\n",
       "      <td>4.7</td>\n",
       "      <td>5.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-05-01</th>\n",
       "      <td>0.088935</td>\n",
       "      <td>4.4</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-01</th>\n",
       "      <td>-0.020300</td>\n",
       "      <td>3.7</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-01</th>\n",
       "      <td>-0.048003</td>\n",
       "      <td>3.7</td>\n",
       "      <td>3.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-10-01</th>\n",
       "      <td>-0.029225</td>\n",
       "      <td>3.2</td>\n",
       "      <td>3.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-01</th>\n",
       "      <td>0.093358</td>\n",
       "      <td>3.1</td>\n",
       "      <td>3.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-01</th>\n",
       "      <td>0.053768</td>\n",
       "      <td>3.4</td>\n",
       "      <td>3.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   r  cpi  lcpi\n",
       "1990-01-01 -0.070114  5.2   4.7\n",
       "1990-02-01  0.014900  5.3   4.6\n",
       "1990-03-01  0.024148  5.2   5.2\n",
       "1990-04-01 -0.028283  4.7   5.3\n",
       "1990-05-01  0.088935  4.4   5.2\n",
       "...              ...  ...   ...\n",
       "2023-08-01 -0.020300  3.7   3.0\n",
       "2023-09-01 -0.048003  3.7   3.2\n",
       "2023-10-01 -0.029225  3.2   3.7\n",
       "2023-11-01  0.093358  3.1   3.7\n",
       "2023-12-01  0.053768  3.4   3.2\n",
       "\n",
       "[408 rows x 3 columns]"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lqreg_data=pd.merge(qreg_data,cpi,left_index=True,right_index=True)\n",
    "lqreg_data=qreg_data['1990':]\n",
    "lqreg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      r   R-squared:                       0.014\n",
      "Model:                            OLS   Adj. R-squared:                  0.012\n",
      "Method:                 Least Squares   F-statistic:                     5.829\n",
      "Date:                Sat, 04 Jan 2025   Prob (F-statistic):             0.0162\n",
      "Time:                        08:38:54   Log-Likelihood:                 690.72\n",
      "No. Observations:                 406   AIC:                            -1377.\n",
      "Df Residuals:                     404   BIC:                            -1369.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0177      0.004      4.215      0.000       0.009       0.026\n",
      "lcpi          -0.0032      0.001     -2.414      0.016      -0.006      -0.001\n",
      "==============================================================================\n",
      "Omnibus:                       31.147   Durbin-Watson:                   1.978\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               45.660\n",
      "Skew:                          -0.551   Prob(JB):                     1.22e-10\n",
      "Kurtosis:                       4.218   Cond. No.                         6.50\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\18762\\AppData\\Local\\Temp\\ipykernel_2160\\3478459724.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  lqreg_data['lcpi']=lqreg_data['cpi'].shift(2)\n"
     ]
    }
   ],
   "source": [
    "lqreg_data['lcpi']=lqreg_data['cpi'].shift(2) \n",
    "lmodel_cpi=smf.ols('r ~ lcpi',data=lqreg_data).fit()\n",
    "print(lmodel_cpi.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 结果解释"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "理论论述与结果不一致\n",
    "\n",
    "\n",
    "股票市场受到多种因素的影响，包括投资者情绪、市场心理等。有时，即使失业率和CPI的变化符合理论预期，但由于市场情绪的波动，股票市场的实际表现可能与理论预测不一致。\n",
    "\n",
    "\n",
    "除了失业率和CPI，还有许多其他经济指标（如GDP、工业产出、消费者信心等）会影响股票市场，当这些指标的变化与失业率和CPI的变化方向不一致时，可能会导致股票市场的表现与理论预期出现偏差。\n",
    "\n",
    "\n",
    "政府和中央银行的政策决策具有一定的不确定性，例如，即使失业率上升，政府可能会采取超出预期的刺激措施，从而对股票市场产生积极影响，与理论预期不一致。\n",
    "\n",
    "在实际分析中，使用的失业率和CPI数据可能存在一定的时效性和准确性问题，如果数据更新不及时或存在误差，可能导致分析结果与理论预期不一致。\n",
    "\n",
    "随着时间的推移，股票市场的结构和参与者也会发生变化，例如，机构投资者的比例增加、高频交易的兴起等，都可能改变市场对失业率和CPI变化的反应机制，从而导致理论与实际分析结果不一致.\n"
   ]
  }
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